% ex3_6.m  to make a series of plots explaining the 
% periodic convolution operation
%
clear, clf, clc, flops(0)
% define the filter IR & input seq. & initialize output seq.
N=20;				% total sequence length
M=6;				% total filter length
L=16; 				% extent parameter of input signal
n=(0:N-1);			% conventional discrete time index
for nr=1:N			% matlab discrete time index
	n1=nr-1;			% conventional index
	if nr<=M
		hr(nr)=0.9*exp(-n1/M);
	else
		hr(nr)=0;
	end
	if  n1>=L/2 & n1<=L  
		xr(nr)=1;
	else
		xr(nr)=0;
	end
end
% initialize the output vector to be -1 for "plotting purposes":
% the output will be computed sequentially for each time and stored.
yr=zeros(1,N)-1;			
% 
for nr=1:N
	clf			% clear figure
	subplot(2,1,1)
	plot(n,xr,'+')
	hold on
	axis([0,N-1,-0.1,1.1])
	xlabel('m (convolution sum index) ')
	ylabel('x(m) and h(n-m)')
	title('Sequences For Computing One Output Value')
	for mr=1:N
% this is the block for the aperiodic convolution
%		if (nr-mr+1>=1) & (nr-mr+1)<=N
%			hrevr(mr)=hr(nr-mr+1);
%		else
%			hrevr(mr)=0;
%		end
% this is the block for the periodic convolution
		hrevr(mr)=hr(pod(nr-mr,N)+1);
	end
	subplot(2,1,1)
	plot(n,hrevr,'ro')
%
	yr(nr)=dot(hrevr,xr);
	subplot(2,1,2)
	plot(n,yr,'cx')
	axis([0,N-1,-0.1,5.1])
	xlabel('n (discrete time) ')
	ylabel('y (filter output)')
%	title('Filter Output')
	drawnow
	disp('press any key to continue to next step')
	pause
end
hold off
disp('the # of flops used is  ')
flops